The fact that millions of young fans look up to her is something music sensation Taylor Swift takes very seriously. In fact, the 21-year-old singer/songwriter tells Lesley Stahl it's a responsibility she has an obligation to handle responsibly. Stahl's profile of the young superstar will be broadcast on "60 Minutes", Sunday, Nov. 20 at 7 p.m. ET/PT.

Swift says she is reminded of her status as role model every day. "I definitely think about a million people when I am getting dressed in the morning," she tells Stahl. "That's just part of my life now. I think it's my responsibility to know it and to be conscious of it."

She eschews the notion that stars aren't responsible for other people's children. "It would be really easy to say...I'm 21 now. I do what I want. You raise your kids. But...that's not the truth of it. The truth of it is that every singer out there with songs on the radio is raising the next generation. So make your words count," says Swift.

Swift practices that mission with songs like "Mean," an attack on cruelty that she originally wrote in response to a painful episode in her own life, but then broadened into an attack on bullying of all types. It's a message her fans embrace while living or remembering the difficult period of adolescence. It's become an anti-meanness anthem.

Swift sings songs like that from experience. She wasn't always the willowy, pretty girl she grew up to be. At one point in her life, she tells Stahl, she wasn't as slim as she wanted to be, nor had hair as straight as she would have liked. She also wore glasses.

There is still some of that awkward child in the woman who now sells millions of records and enthralls thousands in packed venues. "Criticism still hurts. I don't have thick skin. I hate reading criticisms," she says. "You never really, like, get past things hurting you."